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How many different positive, six-digit integers can be formed using the digits 2, 2, 5, 5, 9 and 9?

 Aug 29, 2021
 #1
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2, 2, 5, 5, 9, 9==6 digits ==6!/2!.2!.2!==90 permutations as follows:

 

[(2, 2, 5, 5, 9, 9), (2, 2, 5, 9, 5, 9), (2, 2, 5, 9, 9, 5), (2, 2, 9, 5, 5, 9), (2, 2, 9, 5, 9, 5), (2, 2, 9, 9, 5, 5), (2, 5, 2, 5, 9, 9), (2, 5, 2, 9, 5, 9), (2, 5, 2, 9, 9, 5), (2, 5, 5, 2, 9, 9), (2, 5, 5, 9, 2, 9), (2, 5, 5, 9, 9, 2), (2, 5, 9, 2, 5, 9), (2, 5, 9, 2, 9, 5), (2, 5, 9, 5, 2, 9), (2, 5, 9, 5, 9, 2), (2, 5, 9, 9, 2, 5), (2, 5, 9, 9, 5, 2), (2, 9, 2, 5, 5, 9), (2, 9, 2, 5, 9, 5), (2, 9, 2, 9, 5, 5), (2, 9, 5, 2, 5, 9), (2, 9, 5, 2, 9, 5), (2, 9, 5, 5, 2, 9), (2, 9, 5, 5, 9, 2), (2, 9, 5, 9, 2, 5), (2, 9, 5, 9, 5, 2), (2, 9, 9, 2, 5, 5), (2, 9, 9, 5, 2, 5), (2, 9, 9, 5, 5, 2), (5, 2, 2, 5, 9, 9), (5, 2, 2, 9, 5, 9), (5, 2, 2, 9, 9, 5), (5, 2, 5, 2, 9, 9), (5, 2, 5, 9, 2, 9), (5, 2, 5, 9, 9, 2), (5, 2, 9, 2, 5, 9), (5, 2, 9, 2, 9, 5), (5, 2, 9, 5, 2, 9), (5, 2, 9, 5, 9, 2), (5, 2, 9, 9, 2, 5), (5, 2, 9, 9, 5, 2), (5, 5, 2, 2, 9, 9), (5, 5, 2, 9, 2, 9), (5, 5, 2, 9, 9, 2), (5, 5, 9, 2, 2, 9), (5, 5, 9, 2, 9, 2), (5, 5, 9, 9, 2, 2), (5, 9, 2, 2, 5, 9), (5, 9, 2, 2, 9, 5), (5, 9, 2, 5, 2, 9), (5, 9, 2, 5, 9, 2), (5, 9, 2, 9, 2, 5), (5, 9, 2, 9, 5, 2), (5, 9, 5, 2, 2, 9), (5, 9, 5, 2, 9, 2), (5, 9, 5, 9, 2, 2), (5, 9, 9, 2, 2, 5), (5, 9, 9, 2, 5, 2), (5, 9, 9, 5, 2, 2), (9, 2, 2, 5, 5, 9), (9, 2, 2, 5, 9, 5), (9, 2, 2, 9, 5, 5), (9, 2, 5, 2, 5, 9), (9, 2, 5, 2, 9, 5), (9, 2, 5, 5, 2, 9), (9, 2, 5, 5, 9, 2), (9, 2, 5, 9, 2, 5), (9, 2, 5, 9, 5, 2), (9, 2, 9, 2, 5, 5), (9, 2, 9, 5, 2, 5), (9, 2, 9, 5, 5, 2), (9, 5, 2, 2, 5, 9), (9, 5, 2, 2, 9, 5), (9, 5, 2, 5, 2, 9), (9, 5, 2, 5, 9, 2), (9, 5, 2, 9, 2, 5), (9, 5, 2, 9, 5, 2), (9, 5, 5, 2, 2, 9), (9, 5, 5, 2, 9, 2), (9, 5, 5, 9, 2, 2), (9, 5, 9, 2, 2, 5), (9, 5, 9, 2, 5, 2), (9, 5, 9, 5, 2, 2), (9, 9, 2, 2, 5, 5), (9, 9, 2, 5, 2, 5), (9, 9, 2, 5, 5, 2), (9, 9, 5, 2, 2, 5), (9, 9, 5, 2, 5, 2), (9, 9, 5, 5, 2, 2)] >Total distinct permutations = 90

 Aug 29, 2021

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